标题： 第四后闵可夫斯基阶的引力制动辐射波形和第二后牛顿级水平 显示英文标题

标题： Gravitational Bremsstrahlung Waveform at the fourth Post-Minkowskian order and the second Post-Newtonian level

摘要： 使用多极后闵可夫斯基形式，我们在第四后闵可夫斯基阶（$O(G^4)$，或两环阶）和分数二阶后牛顿精度（$O(v^4/c^4)$）下计算由两个非自旋物体的引力散射产生的频域波形。 波形在自旋加权球谐函数中分解，所需的辐射多极矩，$U_{\ell m}(\omega), V_{\ell m}(\omega)$，以少量主积分明确表示。 主积分的基包含（修改后的）贝塞尔函数以及具有贝塞尔函数源的非齐次贝塞尔方程的解。 我们展示了如何将后者用梅杰G函数表示。 我们检查了结果的低频展开是否符合现有的经典软定理。 我们还通过计算一个物体静止系中辐射能量和动量的$O(G^3)$谱密度，完善了我们之前关于$O(G^2)$制动辐射波形的结果，在速度的第三十阶进行计算。 显示英文摘要

摘要： Using the Multipolar Post-Minkowskian formalism, we compute the frequency-domain waveform generated by the gravitational scattering of two nonspinning bodies at the fourth post-Minkowskian order ($O(G^4)$, or two-loop order), and at the fractional second Post-Newtonian accuracy ($O(v^4/c^4)$). The waveform is decomposed in spin-weighted spherical harmonics and the needed radiative multipoles, $U_{\ell m}(\omega), V_{\ell m}(\omega)$, are explicitly expressed in terms of a small number of master integrals. The basis of master integrals contains both (modified) Bessel functions, and solutions of inhomogeneous Bessel equations with Bessel-function sources. We show how to express the latter in terms of Meijer G functions. The low-frequency expansion of our results is checked againg existing classical soft theorems. We also complete our previous results on the $O(G^2)$ bremsstrahlung waveform by computing the $O(G^3)$ spectral densities of radiated energy and momentum, in the rest frame of one body, at the thirtieth order in velocity.